{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZEIKDTMLTO2INOIX5EYMEX3VEE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3a5766cd7924c0bf51fa899b316a2233689b9daa43972c349b2d2af274c96b24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-21T18:37:13Z","title_canon_sha256":"c3fcb611d08966593a47f811cb71c49cd2391c6c17b5144755950866b3d3b6fe"},"schema_version":"1.0","source":{"id":"1310.5669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5669","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5669v2","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5669","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZEIKDTMLTO2I","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZEIKDTMLTO2INOIX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZEIKDTML","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:6f4a3d0a0f8c8077027abf3927bd24203ebd33f3f46dabeb81ce196fc5d5f477","target":"graph","created_at":"2026-05-18T03:09:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For the Gauss sums which are defined by S_n(a,q) := \\sum_{x (mod q)} e(ax^n/q), Stechkin (1975) conjectured that the quantity A := \\sup_{n,q\\ge 2} \\max_{\\gcd(a,q)=1} |S_n(a,q)|/q^(1-1/n) is finite. Shparlinski (1991) proved that A is finite, but in the absence of effective bounds on the sums S_n(a,q) the precise determination of A has remained intractable for many years. Using recent work of Cochrane and Pinner (2011) on Gauss sums with prime moduli, in this paper we show that with the constant given by A = |S_6(4787,4606056)|/4606056^(5/6) = 4.709236... one has the sharp inequality |S_n(a,q)|","authors_text":"Igor E. Shparlinski, William D. Banks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-21T18:37:13Z","title":"On Gauss sums and the evaluation of Stechkin's constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5669","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c7a90e7d6341c8bac254d45e85dc5a37c46a8d9a66b058830d59821f936bdd1a","target":"record","created_at":"2026-05-18T03:09:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3a5766cd7924c0bf51fa899b316a2233689b9daa43972c349b2d2af274c96b24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-21T18:37:13Z","title_canon_sha256":"c3fcb611d08966593a47f811cb71c49cd2391c6c17b5144755950866b3d3b6fe"},"schema_version":"1.0","source":{"id":"1310.5669","kind":"arxiv","version":2}},"canonical_sha256":"c910a1cd8b9bb486b917e930c25f75213928d7cb2294c002b4434d027fab2904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c910a1cd8b9bb486b917e930c25f75213928d7cb2294c002b4434d027fab2904","first_computed_at":"2026-05-18T03:09:21.652709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:21.652709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rJTU4oYdQmlNsaqJjknJXyEGhIiIy/VAln/6ATmngunACKs8bjCLCDnlFG+6DjDoKK3D12OmlXTc0OFzqNt1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:21.653389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a90e7d6341c8bac254d45e85dc5a37c46a8d9a66b058830d59821f936bdd1a","sha256:6f4a3d0a0f8c8077027abf3927bd24203ebd33f3f46dabeb81ce196fc5d5f477"],"state_sha256":"a5a08a8f1d3c20c42d64fc58653297ea1c3b8680133026c7665276f4feaed286"}